Chaotic spin dynamics of spin-1 Bose-Einstein condensates with broken conservation of magnetization

Spinor Bose-Einstein condensates (BECs) are highly tunable quantum systems and have the potential to generate useful entanglements for enhanced sensing. The spin dynamics of spin-1 BECs have been analytically solved by mapping to a non-rigid pendulum, under the mean-field and single-mode approximations. This study introduces a transverse coupling that breaks integrability by causing magnetization to no longer be conserved. Increasing the coupling strength is expected to cause a transition from regular to chaotic dynamics, which may be identified with a variety of analyses, including of the energy level statistics or out-of-time order correlators. Ground state phase transitions and dynamical phase transitions have been identified by divergence in the quantum Fisher information, which is connected to measurement sensitivity by the Cramer-Rao bound. We seek to characterize the parameters that lead to chaotic spin dynamics and to determine if such a system supports measurement sensitivity beyond the standard quantum limit in the chaotic regime.